Space-charge waves in the wiggler field of a Raman free-electron laser

A waveguide filled with a relativistic electron beam that passes through a helical wiggler magnetic field and a uniform axial magnetic field is considered. The propagation of two types of space-charge waves in this device is analyzed. An electrostatic approximation is employed that is based on Gauss's law and the requirements that the magnetic field of the wave and the curl of the electric field of the wave both be zero in the electron-beam reference frame. These equations transformed into the laboratory reference frame are shown to be more accurate than a system of equations that includes Gauss's law in conventional form. A dispersion relation is derived with the combined effects of the wiggler and axial magnetic fields and the waveguide boundary included. Some numerical results are presented for both plasma and cyclotron types of space-charge waves.